When an object sits on a frictionless incline plane, the two forces acting on the object are the gravitational pull of the earth, its weight, mg, and the supporting force supplied by the surface of the incline, the normal, . These forces are shown in blue.

Since the object slides along the surface of the incline, we need to use the components of its weight, mg, when working problems. The formula used to calculate the component of the weight which acts parallel to the incline's surface is

Fd = mg sin(θ)

In this formula, you can use the mnemonic that the "d" represents "down" which is parallel to the incline.

While the formula used to calculate the component of the weight that acts
perpendicular to the incline's surface is

Fn = mg cos(θ)

In this formula, you can use the mnemonic that the "n" represents "normal" which is perpendicular to the incline.

Let's take a moment and practice using these two preliminary formulas.

Refer to the following information for the next five questions.

A 5-kg mass is placed on an incline titled at 15º.

How much does the 5-kg mass weigh?

Calculate the magnitude of the component that is acting parallel to the incline's surface?

Calculate the magnitude of the component that is acting perpendicular to the incline's surface?

At what angle would these two components be equal in magnitude?

In which range of angles would Fd > Fn? (a) 0º<θ<45º (b) 45º<θ<90º

Usually our problems are more complicated than just calculating the components of the object's weight. Here are some classic situations involving a mass moving along the surface of a frictionless incline.

Refer to the following information for the next four questions.

Suppose that you now want to drag a 5-kg mass up and down a frictionless 15º inclined plane.

How much force must you apply to a string acting parallel to the incline's surface to slide the 5-kg mass up or down the incline at a constant velocity?

How much upward force would be needed to accelerate the 5-kg mass up this incline at 3 m/sec2?

How much upward force would be needed to restrict the 5-kg mass' downward acceleration to 1 m/sec2?

If the 5-kg mass were allowed to slide down this incline without any additional applied forces acting upon it, what would be its acceleration down the incline?